US7330031B2 - Matrix shim system with grouped coils - Google Patents
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- US7330031B2 US7330031B2 US11/506,799 US50679906A US7330031B2 US 7330031 B2 US7330031 B2 US 7330031B2 US 50679906 A US50679906 A US 50679906A US 7330031 B2 US7330031 B2 US 7330031B2
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- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R33/00—Arrangements or instruments for measuring magnetic variables
- G01R33/20—Arrangements or instruments for measuring magnetic variables involving magnetic resonance
- G01R33/28—Details of apparatus provided for in groups G01R33/44 - G01R33/64
- G01R33/38—Systems for generation, homogenisation or stabilisation of the main or gradient magnetic field
- G01R33/387—Compensation of inhomogeneities
- G01R33/3875—Compensation of inhomogeneities using correction coil assemblies, e.g. active shimming
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- the invention relates to a matrix shim system for generating magnetic field components superimposed on a main static magnetic field parallel to a z-axis, wherein said magnetic field components act to homogenize the magnetic field component of the main static magnetic field along the z-axis in a volume of interest, wherein the volume of interest is centered at the origin of the z-axis, and wherein the matrix shim system comprises a plurality of annular coils, the axes of the annular coils coinciding-with the z-axis.
- Nuclear magnetic resonance is a powerful tool in chemical analysis and imaging of samples.
- a sample is positioned in a strong static magnetic field and is subjected to electromagnetic pulses.
- the reaction of the nuclei of the sample is measured and analyzed.
- the characteristics of the static magnetic field influence the quality of information that can be obtained from the sample. In general, best quality is achieved with high field strength and a high homogeneity (uniformity) of the static magnetic field.
- the static magnetic field is generated by a main magnetic coil system, which is, in general, superconducting.
- the main magnetic coil system generates a main static magnetic field with a high field strength, but typically with an insufficiently low homogeneity.
- a shim system is used in order to homogenize the main static magnetic field.
- the shim system generates magnetic field components which, when superimposed to the main static magnetic field, result in an overall static magnetic field with high homogeneity.
- the main static magnetic field B z in a z-direction can be described with a series expansion, with its summands being spherical harmonic functions T nm multiplied with coefficients A nm , with n, m indices of summation.
- m 0.
- the summand A 00 T 00 describes the desired strong magnetic field
- the summand A 10 T 10 describes a field gradient that may be desired or not, according to the intended application and that may be dealt with a set of gradient coils
- all summands A n0 T n0 , with n ⁇ 2 describe undesired inhomogeneities.
- each coil arrangement consisting of a coil or a group of coils.
- Each coil arrangement generates magnetic field components corresponding to one of the spherical harmonic functions.
- each coil arrangement may compensate for exactly one summand A n0 T n0 , with n ⁇ 2, assuming that an appropriate current is chosen within the coil arrangement, according to its so-called gradient strength.
- Each coil arrangement has its own current supply. The more coil arrangements used, the more orders of inhomogeneity which may be compensated.
- a matrix shim system has a plurality of coils, with each coil being fed by its own current source. Each coil contributes to several spherical harmonics.
- the current (and thus the strength of the magnetic field generated) in each coil of the matrix shim system it is possible to homogenize a main static magnetic field up to an order corresponding to the number of coils.
- additional conditions may be respected. Neighboring windings with oppositely running currents, as within a traditional shim systems, may be replaced with one single coil, for example.
- a matrix shim system is much simpler than a traditional shim system.
- matrix shim systems also have disadvantages.
- Each coil has its strongest contribution to the resulting static magnetic field by an A 00 summand.
- the A 00 magnetic field component directly influences the measured spectra. This means that fluctuations in the power supply of any one coil cause side bands or increase the noise floor in measured NMR spectra.
- current sources which are typically digitally controlled, may change their current value only in finite steps. Calculated current values for the coils must be rounded to feasible values. This causes significant deviations from the desired static magnetic field, in particular in the A 00 and the A 10 components.
- a matrix shim system of the above kind characterized in that the matrix shim system comprises g groups G 1 . . . G g of coils, with g being a natural number ⁇ 1, wherein each group G i consists of at least two single annular coils C i1 . . . C ic(i) connected in series, with i: index number of the group, and c(i) being the amount of annular coils within group i, each group G i being designed to generate, in use, a magnetic field
- each group G i of coils has an individual, adjustable electrical current supply (12).
- Conventional matrix shim systems consist of isolated coils, each having an individual power supply. Each coil therefore necessarily contributes significantly to the zero and first order magnetic field components (A 00 and A 10 ).
- groups of coils are built within the matrix shim system, with the coils of a group being connected in series and having the same current supply. Such a group contributes significantly to at least two (but typically many more) higher order magnetic field terms (A 20 or higher).
- the group may be (and preferably is) designed such that the zero and/or first order field components of its coils cancel each other, at least partly. Thus the group's contribution to the resulting static magnetic field in these components is reduced.
- the NMR spectrum is less deteriorated then, as compared to known matrix shim systems.
- a group of the inventive matrix shim system not only contributes to one order of the magnetic field, but to several. This allows much more freedom in the construction of a group, as compared to a coil arrangement of a traditional shim system.
- the invention there is no need to place coils of two groups in identical spaces, or to place coils with opposite windings close to each other. The latter makes the inventive matrix shim system very power-efficient.
- each of these remaining single coils has an individual current supply. Note that the total number of current supplies indicates the maximum number of orders of the magnetic field that can be homogenized with the inventive matrix shim system.
- the radius R basically corresponds to the value of the diameter of the volume of interest.
- R n in the expression A n0 (G i ) ⁇ R n the expression has a uniform dimension of a magnetic field strength, independent of the value of the index n.
- the expressions of different values of n are made comparable.
- a preferred embodiment is characterized in that g ⁇ 4, in particular wherein g ⁇ 10.
- a larger amount of groups allows a higher number of orders of field components to be homogenized, and/or more degrees of freedom for additional side conditions.
- each annular coil C is belonging to a group G i is designed to generate, in use, a magnetic field
- ⁇ ⁇ s 1 c ⁇ ( i ) ⁇ A 00 ⁇ ( C is ) ⁇ max ⁇ ⁇ ⁇ A 00 ⁇ ( C i ⁇ ⁇ 1 ) ⁇ , ... ⁇ , ⁇ A 00 ⁇ ( C ic ⁇ ( i ) ) ⁇ ⁇ ⁇ 0.5 , with s: coil index within a group of coils. In other words, within a group of coils, the largest contribution to A 00 of one of the coils is compensated by the other coils of this group by at least 50%. This reduces the susceptibility of the matrix shim system to current fluctuations.
- each annular coil C is belonging to a group G i is designed to generate, in use, a magnetic field
- ⁇ ⁇ s 1 c ⁇ ( i ) ⁇ A 10 ⁇ ( C is ) ⁇ max ⁇ ⁇ ⁇ A 10 ⁇ ( C i ⁇ ⁇ 1 ) ⁇ , ... ⁇ , ⁇ A 10 ⁇ ( C ic ⁇ ( i ) ) ⁇ ⁇ ⁇ 0.5 , with s: coil index within a group of coils. In other words, within a group of coils, the largest contribution to A 10 of one of the coils is compensated by the other coils of this group by at least 50%. This also reduces the susceptibility of the matrix shim system to current fluctuations.
- the coil C k1 has a winding number of N k1
- the group G k1 consisting of only two coils, is very simple and the two lowest order spherical harmonics (A 00 and A 10 ) of the two coils cancel almost exactly.
- another further development of said embodiment is characterized in that the z-positions and ratio of winding numbers of the coils of the group G k are adjusted such that changing the current in these coils has strong indirect influence on the magnetic field in the volume of interest, in particular by causing eddy currents, by changing the magnetization of ferromagnetic or superconducting materials or by coupling to a closed superconducting loop.
- the matrix shim system may be shielded.
- At least one group G m of the groups G 1 . . . G g consists of two annular coils C m1 , C m2 both having a radius of a m and a winding number of N m , the coil C m1 being wound in the other direction as coil C m2 , wherein the coil C m1 is located at a z-position t m1 , and the coil C m2 is located at a z-position t m2 , with
- the group G m consisting of only two coils, is very simple and the two lowest order spherical harmonics (A 00 and A 10 ) of the coils cancel almost exactly.
- the matrix shim system comprises to additional coils that produce magnetic fields that are not axially symmetric with respect to the z-axis.
- the matrix shim system comprises a means for performing an algorithm, which determines the necessary currents to be supplied to the coils of the matrix shim system in order to homogenize the magnetic field component along the z-axis in the volume of interest. In this case, no external means for said algorithm is necessary.
- the algorithm determines the currents such that indirect influences on the magnetic field in the volume of interest are minimized by using groups of coils to compensate for indirect influences of other coils.
- the algorithm determines the currents such that the amount of heat produced by the coils is minimized. This keeps costs for cooling small.
- all annular coils of the matrix shim system belong to one of the groups G 1 . . . G g .
- the matrix shim system is particularly stable against current fluctuations.
- w N defines the relative importance of suppression or production of the spherical harmonic
- p 0 , p 1 , . . . , p N define the relative importance of small versus big terms
- F not — G is the cost function for all coils that are not built as groups of coils G i ;
- the method provides a robust and simple way to design an inventive matrix shim system.
- the parameters describing the coil are selected such that coil conditions are automatically fulfilled which reduce the total number of parameters. In this way, the complexity of the numerical problem to be solved can be reduced, and therefore the amount of time and computer power that has to be spent in order to find a usable result can also be reduced.
- Another variant of the inventive method is characterized in that the numerical optimization algorithm involves any of the following methods: gradient descent method, conjugated gradient method, simulated annealing, evolutionary optimization and genetic optimization. These listed methods have turned out to be useful in practice.
- FIG. 1 schematically shows a single annular coil C described by its radius a and its z-position zc with respect to the center of the volume of interest;
- FIG. 2 schematically shows a group of annular coils connected in series and fed by one power supply, in accordance with the invention; the case illustrated here is the case of a group consisting of two coils C 1 and C 2 positioned at z 1 and z 2 respectively and having opposite winding directions;
- FIG. 3 shows a diagram of the normalized contribution of a single annular coil to spherical harmonics A n0 as a function of the z position; the numbers 1 to 6 denote n of the curve belonging to A n0 ;
- FIG. 4 shows a diagram correlating the z positions of a pair of coils, as calculated as solutions for pairs (z 1 ,z 2 ) of z-positions according equations (5,6);
- FIG. 5 schematically shows a configuration of coils of a traditional shim system of prior art; each channel, i.e. each combination of coils connected in series and fed by one current source, is shown on a separate row;
- FIG. 6 schematically shows a configuration of coils of a matrix shim system of prior art; each channel, i.e. each combination of coils connected in series and fed by one current source, is shown on a separate row;
- FIG. 7 schematically shows a configuration of coils of an inventive matrix shim system comprising five groups G 1 , . . . , G 5 and a gradient coil combination; each channel, i.e. each combination of coils connected in series and fed by one current source, is shown on a separate row;
- FIG. 8 shows a diagram of the magnetic fields of single coils at z-position z 1 (dashed curves) compared to the magnetic fields of the same coils combined with additional coils at z-position z 2 that eliminate A 0 and A 1 components (solid curves);
- FIG. 9 b schematically shows two examples of groups G m of two coils C m1 , C m2 at z positions t m1 , t m2 with
- FIG. 9 c schematically shows three examples of groups G p of three coils C p1 , C p2 , C p3 at z positions t p1 , t p2 , t p3 with winding numbers N p1 , N p2 , N p3 , with
- /a ⁇ 0.5 and N p1 +N p3 N p2 , suppressing A 00 and A 10 coefficients of the group G p .
- the invention relates to an electrical current shim system.
- Supplying electrical current to a set of spirally wound coils generates corrective magnetic field components of cylindrical symmetry.
- At least some of the power supplies are connected to a group of at least two annular coils, connected in series.
- the positions and number of windings of such a group of annular coils is selected such that the resulting magnetic field fulfills certain conditions with high accuracy and temporal stability without relying on the accuracy and temporal stability of the power supply, but fulfills the condition purely by its geometrical configuration.
- Such conditions are e.g. to produce no field component parallel to the main magnetic field in the volume of interest or to produce no first order field gradient in the volume of interest.
- Several of these elementary groups of coils are supplied with currents in order to produce shim functions, i.e. magnetic fields of a desired spatial distribution.
- the positions and number of windings of an elementary group of annular coils is additionally selected such that the field produced by this group of coils is able to contribute to more than one shim function.
- the type of shim function is determined by the ratios among the currents supplied to each group of coils.
- the whole set of current ratios for all shim functions is called the current matrix. This current matrix can be determined in such a way that the power consumption is minimized.
- the present invention relates to an apparatus generating corrective magnetic fields in a volume of interest where high magnetic field uniformity and high magnetic field stability is required such as for instruments for nuclear magnetic resonance.
- NMR nuclear magnetic resonance
- isotope effects on the NMR chemical shift of the order of 0.17 parts per billion have been reported [2].
- a set of coils to which a control device supplies electrical current produces the desired corrective magnetic field.
- Such devices are routinely used to achieve high field uniformity. They are known as electrical current shims [1] or shim coils.
- ⁇ denotes the Laplace operator which is defined by
- ⁇ ⁇ ⁇ u ⁇ 2 ⁇ x 2 ⁇ u + ⁇ 2 ⁇ y 2 ⁇ u + ⁇ 2 ⁇ z 2 ⁇ u
- the corresponding shim coils are termed ‘zonal shims’ and are constructed as annular coils.
- the other spherical harmonics (m ⁇ 0) are known as ‘tesseral harmonics’ and the shim coils producing these are ‘tesseral shims’ which are produced e.g. by saddle-type coils.
- FIG. 5 A schematic depiction of a coil configuration used to produce fields of cylindrical symmetry is shown in FIG. 5 .
- the signs indicate the winding directions.
- Equation (2) contains infinitely many terms whereas any technical realization only can provide a finite set of correction coils.
- Low orders n of spherical harmonics are relatively easy to create. The higher the order n gets, the more difficulties arise to provide a field with significant strength in the form of the desired spherical harmonic. The more terms in equation (2) which can be corrected, the higher is the uniformity of the magnetic field. Therefore a great deal of effort has been made in order to push the highest correctable order to ever-higher values.
- FIG. 3 shows the normalized (i.e. after removing the dependency from the coil radius a) contribution of a single annular coil at position z to the coefficient A n0 . This figure shows that most of the contributions to high order coefficients A n0 come from a region
- the solution to this problem is the use of a matrix shim system [5].
- the basic idea is to use simple coils, each of them fed by its own current source. Every coil contributes to several spherical harmonics. By selecting certain ratios among the currents in the different coils, different types of correcting fields can be produced. Matrix shim systems are particularly power-efficient in cases where a conventional system would use currents flowing in opposite directions in closely neighboring windings of different coils. Both currents dissipate power but the fields close to these windings nearly cancel each other.
- FIG. 1 shows an elementary coil
- FIG. 6 shows an example of a coil configuration used for the cylindrical symmetric part of a matrix shim system.
- Lagrangian shims Shim functions using such a configuration of shim coils carrying a current determined by using Lagrangian multipliers to fulfill an additional condition are named Lagrangian shims and are described in [4].
- Simple coils mainly contribute to the A 00 term that must stay constant.
- FIG. 8 the contribution of single coils to the A 00 component (B z 0 (0)) can be seen (dashed curves).
- the ratios among the currents in the different coils are selected in a way that no net contribution to A 00 occurs in summation of all coils. If any of the current sources not exactly supply the current it is supposed to, the deviation from the ideal field is mainly described by A 00 . If such a deviation from the ideal current value is time dependent, it produces, in the case of magnetic resonance techniques, a modulation of the phase of the acquired signal.
- the idea behind the inventive matrix shim system is to replace some of the single annular coils of the conventional matrix shim system by groups of two and more annular coils connected in series, where the z-positions and winding numbers of the annular coils within one group are adjusted such that the low orders of spherical harmonics are suppressed and at the same time several high orders of spherical harmonics are generated with high efficiency, and that this condition is achieved solely by the geometrical configuration of the coils defining the group.
- the single coils as well as the groups of coils are energized by individually adjustable currents (this is a characteristic property of matrix shim systems) such that their integral effect produces the desired correcting field.
- This new matrix shim system also containing groups of coils instead of only single coils, has the great advantage that the low orders of spherical harmonics, which are normally generated when high orders of spherical harmonics are desired, are compensated by the geometrical configuration of the coils within the group and not by high currents in different single coils which is the case in conventional matrix shim systems. It is important to note that the necessary geometrical stability is much easier to achieve than the necessary current stability.
- inventive matrix shim system The basic idea behind the inventive matrix shim system is first described by discussing the properties of the simplest case of such a group of coils, namely a pair of ideally thin coils, and then extended to coils using a finite volume and groups containing more than two coils.
- a pair of coils can be constructed such that the two lowest orders of spherical harmonics, i.e. A 00 and A 10 , cancel exactly and that there are still enough degrees of freedom to support different higher order spherical harmonics.
- ⁇ z _ 2 ⁇ 1 / z _ 1 ⁇ z _ 1 ( 5 )
- I 2 ⁇ - I 1 / ⁇ z _ 1 ⁇ 3 - I 1 ( 6 )
- the second (trivial) solution describes two counter-wound coils at exactly the same position creating no field at all.
- a pair of coils producing a field according to condition (3) must consist of two coils located on the same side of the center of the volume of interest and have opposite polarity. Additionally, if one of the coils is in the interval 0 ⁇
- the second coil needs to be located on the same side of the center of the volume of interest and have opposite polarity.
- the A 10 component is already zero.
- two symmetrically positioned, coils with opposite winding direction compared to the first coil are necessary.
- a coil may be constructed by placing blocks of windings centered around z 1 and z 2 determined as described above and using winding numbers N 1 , N 2 wound in opposite direction and connected in series.
- the ratio N 1 :N 2 should be a good approximation to
- 1/
- the electrical power needed to produce a given field distribution is inversely proportional to the total cross section of the coil. Therefore the cross section of the coils should be increased as much as is compatible with other restrictions. Taking the limitations in voltage and current of the current supplies into account, available space in radial and axial direction can be filled up using an appropriate wire gauge.
- the first conditions may rather be imposed on the average value of the field instead of the value at the center.
- the second condition may be imposed to the difference of the field at opposite ends of the volume of interest rather then on the first derivative with respect to z. Changing conditions in this way may require another slight correction to the ideal solution.
- FIG. 7 schematically shows a configuration of coils of an inventive matrix shim system.
- Each channel i.e. each combination of coils connected in series and fed by one current source, is shown on a separate row.
- the inventive matrix shim system contains one combination 71 of annular coils to generate a 1 st order gradient (see lowest row). All other annular coils in the matrix shim system belong to one of the groups G 1 , . . . , G 5 .
- FIGS. 9 a through 9 c schematically shows possible configurations for groups of coils constructed such that they suppress A 00 and A 10 coefficients of the respective group.
- a typical matrix shim system in accordance with the invention comprises several of such groups. Each example of a group with its coils is shown in a different row. For simplification, reference signs are only placed at the example shown in the uppermost respective row.
- the radius a is the radius of each group of coils and is shown as a unit of measurement on the z-axis.
- FIG. 9 b shows two examples of groups G m of two annular coils C m1 and C m2 , both having a radius a and a winding number N m .
- the coil C m1 is wound in the other direction as coil C m2 .
- the coils C m1 , C m2 are located at z positions t m1 and t m2 , with
- FIG. 9 c shows three examples of groups G p of three annular coils C p1 , C p2 , C p3 . All coils C p1 , C p2 , C p3 have the same radius a, have winding numbers N p1 , N p2 , N p3 , and have z positions t p1 , t p2 , t p3 , with t p1 ⁇ t p2 ⁇ t p3 .
- coils that eliminate the A 00 and A 10 component as is described above A 00 A 10 -free coils.
- a 00 A 10 -free coils To produce all necessary shim functions it is not enough to use only A 00 A 10 -free coils. In most cases a coil is needed that enables to remove an A 10 component.
- a conventionally designed coil producing A 10 can be added to a set of A 00 A 10 -free coils.
- Low orders of A n0 such as A 20 , A 30 , may be more efficiently generated by conventional designs. In these cases an ideal combination of coils contains coils in a conventional design to produce the low order components and a set of A 00 A 10 -free coils, all of which are freely combinable to produce the higher order components.
- Additional coils can be added to produce fields that are not invariant under rotation to produce tesseral harmonic functions.
- a 00 A 10 -free coil pairs according the first solution of (5,6) have an additional interesting property: Keeping the number of turns of the inner coil fixed, the number of turns of the outer coil increases rapidly (I 2 ⁇ z 2 3 ) with increasing z 2 .
- the second coil therefore creates a relatively strong field outside the shim system while having relatively small effects in the volume of interest.
- changing currents in the shim coils can have indirect influences on the magnetic field in the volume of interest, e.g. by causing eddy-currents in the surrounding conducting materials, by changing the magnetization of ferromagnetic or superconducting materials or by coupling to a closed superconducting loop.
- a 00 A 10 -free coil pairs can be used to at least partially compensate for such effects without compromising the quality of the fields used for shimming. I.e. if a change in shim currents has an unwanted effect on the surrounding of the shim system, A 00 A 10 -free coil pairs can act as shielding coils.
- a 70 , A 80 , etc. with increasingly smaller distances between the extremal values.
- the positions of the elementary coils of a three coil system, as described above, are preferably selected such that they match three neighboring extremal values of high order spherical harmonics.
- the total number of parameters involved in the optimization defines the complexity of the problem and therefore the amount of time and computer power that has to be spent in order to find a usable result.
- a matrix shim system for generating magnetic field components superimposed on a main static magnetic field comprising a plurality of annular coils, is characterized in that it comprises g groups G 1 . . . G g of coils, with g being a natural number ⁇ 1, wherein each group G i consists of at least two single annular coils connected in series, wherein each group G i is designed to generate, in use, a magnetic field
Abstract
For each group Gi, there are at least two values of n for which
with N: the total number of current supplies of the matrix shim system, and R: smallest inside radius of any of the annular coils of the matrix shim system. An individual, adjustable electrical current supply is provided for each group Gi of coils. The inventive matrix shim system is both simple in design and stable against current fluctuations.
Description
with An0: series coefficients of order n and
B max(G i)=max {|A 20(G i)·R 2 |, . . . ,|A N0(G i)·R N|},
and, for each group Gi, there are at least two values of n for which
with N: the total number of current supplies connected to annular coils of the matrix shim system, and R: smallest inside radius of any of the annular coils of the matrix shim system. Moreover, each group Gi of coils has an individual, adjustable electrical current supply (12).
For typical inventive matrix shim systems,
will be between 100 to 1000, and
will be between 10 to 100. When the groups comply with these conditions, then the contributions to the lower order field components (A00 and A10) are negligible compared with the higher order field components corresponding to the two values of n. The NMR measurement cannot be disturbed significantly by a current fluctuation.
and that for all groups Gi,
with s: coil index within a group of coils. In other words, within a group of coils, the largest contribution to A00 of one of the coils is compensated by the other coils of this group by at least 50%. This reduces the susceptibility of the matrix shim system to current fluctuations.
and that for all groups Gi,
with s: coil index within a group of coils. In other words, within a group of coils, the largest contribution to A10 of one of the coils is compensated by the other coils of this group by at least 50%. This also reduces the susceptibility of the matrix shim system to current fluctuations.
The group Gm, consisting of only two coils, is very simple and the two lowest order spherical harmonics (A00 and A10) of the coils cancel almost exactly.
For this group Gp, the two lowest order spherical harmonics (A00 and A10) of the coils cancel almost exactly.
In this case, the susceptibility of the inventive matrix shim system to current fluctuations is even lower, since the second order field gradient of the resultant static magnetic field may not fluctuate significantly.
-
- defining parameters describing the coil geometries;
- defining ranges of feasible values for said parameters;
- defining a cost function F to be minimized, this cost function being calculated for any combination of values for said parameters and is constructed such that lower values resulting from the function evaluation reflect an improvement in the coil design, the cost function F containing terms of the form
wherein w0, w1, . . . , wN defines the relative importance of suppression or production of the spherical harmonic, p0, p1, . . . , pN define the relative importance of small versus big terms, Fnot
-
- applying a numerical optimization algorithm in order to find a set of parameters that define a minimum of F.
Δu=0 (1)
with the spherical harmonic functions Tnm
T n0(r,θ,φ)=r n P n(cos θ), for m=0
T nm(r,θ,φ)=r n P nm(cos θ)cos mφ, for m>0
T nm(r,θ,φ)=r n P n|m|(cos θ)sin |m|φ, for m<0
where n, m are integers, Pn is the Legendre polynomial of order n, Pnm is the associated Legendre polynomial of order n and degree m and Anm are coefficients. In this formulation, creating a uniform magnetic field in the volume of interest is equivalent to achieve the condition Anm=0 and for all n, m with the only exception A00=Bz 0.
Anm corr=GnmInm
where Gnm is the so-called gradient strength of the coil and Inm is the current supplied to the coil. Creating a uniform field is now achieved by adjusting the currents Inm such that the correcting magnetic fields cancel the residual field components Anm res:
A nm res +G nm I nm=0
Available space in this region must be distributed carefully.
-
- 1. a change in the current flowing through the coils does not lead to a change in the z-component of the magnetic field at the center of the volume of interest;
- 2. a change in the current flowing through the coils does not lead to a change in the first derivative with respect to z of the magnetic field at the center of the volume of interest.
where
-
- 1. Counter-wound pair of coils connected in series at positions
z 1,1/z 1 - 2. Counter-wound pair of coils connected in series at closely spaced z-positions
- 3. Three coils connected in series, where the two outer coils have opposite winding direction compared to the inner coil.
- 1. Counter-wound pair of coils connected in series at positions
-
- Defining parameters describing the coil geometries
- Defining ranges of feasible values for said parameters
- Defining a cost function F to be minimized where this cost function can be calculated for any combination of values for said parameters and is constructed such that lower values resulting from the function evaluation reflect an improvement in the coil design. Minimization is not a restriction: if a certain property of the system should be maximized it can be incorporated into F as negative summand.
- Applying a numerical optimization algorithm in order to find a set of parameters that define a minimum of F. Among known algorithms that provide the desired functionality are e.g. gradient descent method, conjugated gradient method, simulated annealing, evolutionary optimization and genetic optimization. The latter three methods are particularly suited to handle discrete parameters.
that for each group Gi, there are at least two values of n for which
with N: the total number of current supplies of the matrix shim system, and R: smallest inside radius of any of the annular coils of the matrix shim system, and that for each group Gi of coils, an individual, adjustable electrical current supply (12) is provided. The inventive matrix shim system is both simple in design and stable against current fluctuations.
- 11 volume of interest
- 12 current supply
- 13 diameter of the volume of interest perpendicular to the z direction
- 71 first order gradient coil combination
- G1, G2, G3, . . . groups with
index numbers - C11, C12, C13, . . . coils with
index numbers index number 1
- [1] Anderson W A. Electrical current shims for correcting magnetic Fields. Rev. Sci. Instrum. 32 (1961), March, Nr. 3, 241-250
- [2] Anet F A L, Kopelevich M. Ultrahigh Resolution in Proton NMR Spectra at 500 MHz: Two-Bond Intrinsic Chlorine and Silicon Isotope Effects. J. Am. Chem. Soc. 109 (1987), 5870-5871
- [3] Gang R E. Apparatus for Improving the Uniformity of Magnetic Fields. U.S. Pat No. 3,287,630 (1966).
- [4] Ishikawa H. Apparatus for Generating Corrective Magnetic Field. U.S. Pat No. 5,661,401 (1997).
- [5] Konzbul P, {hacek over (S)}véda K, Srnka A. Design of Matrix Shim Coils System for Nuclear Magnetic Resonance. IEEE Transactions on Magnetics 36 (2000), Nr. 4, 1732-1736.
Claims (22)
B max(G i)=max{|A 20(G i)·R 2 |, . . . , |A N0(G i)·R N|},
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EP05019176A EP1760481B1 (en) | 2005-09-03 | 2005-09-03 | Matrix shim system with grouped coils |
EP05019176.6 | 2005-09-03 |
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EP2146215A1 (en) | 2008-07-18 | 2010-01-20 | Bruker BioSpin AG | Apparatus for executing DNP-NMR measurements with compensation assembly and method for aligning the compensation assembly |
US9638776B2 (en) | 2014-08-22 | 2017-05-02 | General Electric Company | Nested coil configuration of active shims in MRI systems |
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DE602005021356D1 (en) | 2010-07-01 |
EP1760481A1 (en) | 2007-03-07 |
US20070052420A1 (en) | 2007-03-08 |
JP2007078682A (en) | 2007-03-29 |
JP4733602B2 (en) | 2011-07-27 |
EP1760481B1 (en) | 2010-05-19 |
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